Answer
$\frac{6(\frac{2}{\sqrt3}-1)}{\pi}.$
Work Step by Step
The general formula for average rate of change from $a$ to $b$: $\frac{f(b)-f(a)}{b-a}.$
Hence here: $\frac{sec(\frac{\pi}{6})-sec(0)}{\frac{\pi}{6}-0}=\frac{\frac{2}{\sqrt3}-1}{\frac{\pi}{6}}=\frac{6(\frac{2}{\sqrt3}-1)}{\pi}.$